Author: Ben Bolker

# The phylo4 classes and methods

#### Ben Bolker

#### Peter Cowan

#### François Michonneau

    library(phylobase)

## Introduction

This document describes the new ‘phylo4’ S4 classes and methods, which are intended to provide a unifying standard for the representation of phylogenetic trees and comparative data in R. The `phylobase` package was developed to help both end users and package developers by providing a common suite of tools likely to be shared by all packages designed for phylogenetic analysis, facilities for data and tree manipulation, and standardization of formats.

This standardization will benefit end-users by making it easier to move data and compare analyses across packages, and to keep comparative data synchronized with phylogenetic trees. Users will also benefit from a repository of functions for tree manipulation, for example tools for including or excluding subtrees (and associated phenotypic data) or improved tree and data plotting facilities. `phylobase` will benefit developers by freeing them to put their programming effort into developing new methods rather than into re-coding base tools. We (the `phylobase` developers) hope `phylobase` will also facilitate code validation by providing a repository for benchmark tests, and more generally that it will help catalyze community development of comparative methods in R.

A more abstract motivation for developing `phylobase` was to improve data checking and abstraction of the tree data formats. `phylobase` can check that data and trees are associated in the proper fashion, and protects users and developers from accidently reordering one, but not the other. It also seeks to abstract the data format so that commonly used information (for example, branch length information or the ancestor of a particular node) can be accessed without knowledge of the underlying data structure (i.e., whether the tree is stored as a matrix, or a list, or a parenthesis-based format). This is achieved through generic `phylobase` functions which which retrieve the relevant information from the data structures. The benefits of such abstraction are multiple: (1) easier access to the relevant information via a simple function call (this frees both users and developers from learning details of complex data structures), (2) freedom to optimize data structures in the future without breaking code. Having the generic functions in place to “translate” between the data structures and the rest of the program code allows program and data structure development to proceed somewhat independently. The alternative is code written for specific data structures, in which modifications to the data structure requires rewriting the entire package code (often exacting too high a price, which results in the persistence of less-optimal data structures). (3) providing broader access to the range of tools in `phylobase`. Developers of specific packages can use these new tools based on S4 objects without knowing the details of S4 programming.

The base ‘phylo4’ class is modeled on the the `phylo` class in `ape`. and extend the ‘phylo4’ class to include data or multiple trees respectively. In addition to describing the classes and methods, this vignette gives examples of how they might be used.

## Package overview

The phylobase package currently implements the following functions and data structures:

- Data structures for storing a single tree and multiple trees: and ?

- A data structure for storing a tree with associated tip and node data:

- A data structure for storing multiple trees with one set of tip data:

- Functions for reading nexus files into the above data structures

- Functions for converting between the above data structures and objects as well as `phylog` objects (although the latter are now deprecated …)

- Functions for editing trees and data (i.e., subsetting and replacing)

- Functions for plotting trees and trees with data

## Using the S4 help system

The help system works similarly to the help system with some small differences relating to how methods are written. The function is a good example. When we type we are provided the help for the default plotting function which expects `x` and `y`. `R` also provides a way to smartly dispatch the right type of plotting function. In the case of an object (a class object) `R` evaluates the class of the object and finds the correct functions, so the following works correctly.

    library(ape)
    set.seed(1)  ## set random-number seed
    rand_tree <- rcoal(10) ## Make a random tree with 10 tips
    plot(rand_tree)

However, typing still takes us to the default `plot` help. We have to type to find what we are looking for. This is because generics are simply functions with a dot and the class name added.

The generic system is too complicated to describe here, but doesn’t include the same dot notation. As a result doesn’t work, `R` still finds the right plotting function.

    library(phylobase)
    # convert rand_tree to a phylo4 object
    rand_p4_tree <- as(rand_tree, "phylo4")
    plot(rand_p4_tree)

All fine and good, but how to we find out about all the great features of the `phylobase` plotting function? `R` has two nifty ways to find it, the first is to simply put a question mark in front of the whole call:

    `?`(plot(rand_p4_tree))

`R` looks at the class of the object and takes us to the correct help file (note: this only works with objects). The second ways is handy if you already know the class of your object, or want to compare to generics for different classes:

    `?`(method, plot("phylo4"))

More information about how documentation works can be found in the methods package, by running the following command.

    help('Documentation', package="methods")

## Trees without data

You can start with a tree — an object of class `phylo` from the `ape` package (e.g., read in using the `read.tree()` or `read.nexus()` functions), and convert it to a `phylo4` object.

For example, load the raw Geospiza data:

    library(phylobase)
    data(geospiza_raw) # what does it contain?
    names(geospiza_raw)
    #> [1] "tree" "data"

Convert the `S3` tree to a `S4 phylo4` object using the `as()` function:

    (g1 <- as(geospiza_raw$tree, "phylo4"))
    #>           label node ancestor edge.length node.type
    #> 1    fuliginosa    1       24     0.05500       tip
    #> 2        fortis    2       24     0.05500       tip
    #> 3  magnirostris    3       23     0.11000       tip
    #> 4   conirostris    4       22     0.18333       tip
    #> 5      scandens    5       21     0.19250       tip
    #> 6    difficilis    6       20     0.22800       tip
    #> 7       pallida    7       25     0.08667       tip
    #> 8      parvulus    8       27     0.02000       tip
    #> 9    psittacula    9       27     0.02000       tip
    #> 10       pauper   10       26     0.03500       tip
    #> 11   Platyspiza   11       18     0.46550       tip
    #> 12        fusca   12       17     0.53409       tip
    #> 13 Pinaroloxias   13       16     0.58333       tip
    #> 14     olivacea   14       15     0.88077       tip
    #> 15         <NA>   15        0          NA      root
    #> 16         <NA>   16       15     0.29744  internal
    #> 17         <NA>   17       16     0.04924  internal
    #> 18         <NA>   18       17     0.06859  internal
    #> 19         <NA>   19       18     0.13404  internal
    #> 20         <NA>   20       19     0.10346  internal
    #>  [ reached 'max' / getOption("max.print") -- omitted 7 rows ]

The (internal) nodes appear with labels because they are not defined:

    nodeLabels(g1)
    #> 15 16 17 18 19 20 21 22 23 24 25 26 27
    #> NA NA NA NA NA NA NA NA NA NA NA NA NA

You can also retrieve the node labels with .

A simple way to assign the node numbers as labels (useful for various checks) is

    nodeLabels(g1) <- paste("N", nodeId(g1, "internal"), sep="")
    head(g1, 5)
    #>          label node ancestor edge.length node.type
    #> 1   fuliginosa    1       24     0.05500       tip
    #> 2       fortis    2       24     0.05500       tip
    #> 3 magnirostris    3       23     0.11000       tip
    #> 4  conirostris    4       22     0.18333       tip
    #> 5     scandens    5       21     0.19250       tip

The method gives a little extra information, including information on the distribution of branch lengths:

    summary(g1)
    #>
    #>  Phylogenetic tree : g1
    #>
    #>  Number of tips    : 14
    #>  Number of nodes   : 13
    #>  Branch lengths:
    #>         mean         : 0.1764008
    #>         variance     : 0.04624379
    #>         distribution :
    #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
    #> 0.00917 0.04985 0.08000 0.17640 0.21912 0.88077

Print tip labels:

    tipLabels(g1)
    #>              1              2              3              4              5              6
    #>   "fuliginosa"       "fortis" "magnirostris"  "conirostris"     "scandens"   "difficilis"
    #>              7              8              9             10             11             12
    #>      "pallida"     "parvulus"   "psittacula"       "pauper"   "Platyspiza"        "fusca"
    #>             13             14
    #> "Pinaroloxias"     "olivacea"

(`labels(g1,"tip")` would also work.)

You can modify labels and other aspects of the tree — for example, to convert all the labels to lower case:

    tipLabels(g1) <- tolower(tipLabels(g1))

You could also modify selected labels, e.g. to modify the labels in positions 11 and 13 (which happen to be the only labels with uppercase letters):

    tipLabels(g1)[c(11, 13)] <- c("platyspiza", "pinaroloxias")

Note that for a given tree, `phylobase` always return the `tipLabels` in the same order.

Print node numbers (in edge matrix order):

    nodeId(g1, type='all')
    #>  [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Does it have information on branch lengths?

    hasEdgeLength(g1)
    #> [1] TRUE

It does! What do they look like?

    edgeLength(g1)
    #>   15-16   16-17   17-18   18-19   19-20   20-21   21-22   22-23   23-24    24-1    24-2
    #> 0.29744 0.04924 0.06859 0.13404 0.10346 0.03550 0.00917 0.07333 0.05500 0.05500 0.05500
    #>    23-3    22-4    21-5    0-15    20-6   19-25    25-7   25-26   26-27    27-8    27-9
    #> 0.11000 0.18333 0.19250      NA 0.22800 0.24479 0.08667 0.05167 0.01500 0.02000 0.02000
    #>   26-10   18-11   17-12   16-13   15-14
    #> 0.03500 0.46550 0.53409 0.58333 0.88077

Note that the root has `<NA>` as its length.

Print edge labels (also empty in this case — therefore all `NA`):

    edgeLabels(g1)
    #> 15-16 16-17 17-18 18-19 19-20 20-21 21-22 22-23 23-24  24-1  24-2  23-3  22-4  21-5  0-15
    #>    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
    #>  20-6 19-25  25-7 25-26 26-27  27-8  27-9 26-10 18-11 17-12 16-13 15-14
    #>    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA

You can also use this function to label specific edges:

    edgeLabels(g1)["23-24"] <- "an edge"
    edgeLabels(g1)
    #>     15-16     16-17     17-18     18-19     19-20     20-21     21-22     22-23     23-24
    #>        NA        NA        NA        NA        NA        NA        NA        NA "an edge"
    #>      24-1      24-2      23-3      22-4      21-5      0-15      20-6     19-25      25-7
    #>        NA        NA        NA        NA        NA        NA        NA        NA        NA
    #>     25-26     26-27      27-8      27-9     26-10     18-11     17-12     16-13     15-14
    #>        NA        NA        NA        NA        NA        NA        NA        NA        NA

The edge labels are named according to the nodes they connect (ancestor-descendant). You can get the edge(s) associated with a particular node:

    getEdge(g1, 24) # default uses descendant node
    #>      24
    #> "23-24"
    getEdge(g1, 24, type="ancestor") # edges using ancestor node
    #>     24     24
    #> "24-1" "24-2"

These results can in turn be passed to the function to retrieve the length of a given set of edges:

    edgeLength(g1)[getEdge(g1, 24)]
    #> 23-24
    #> 0.055
    edgeLength(g1)[getEdge(g1, 24, "ancestor")]
    #>  24-1  24-2
    #> 0.055 0.055

Is it rooted?

    isRooted(g1)
    #> [1] TRUE

Which node is the root?

    rootNode(g1)
    #> N15
    #>  15

Does it contain any polytomies?

    hasPoly(g1)
    #> [1] FALSE

Is the tree ultrametric?

    isUltrametric(g1)
    #> [1] TRUE

You can also get the depth (distance from the root) of any given node or the tips:

    nodeDepth(g1, 23)
    #> Warning: 'nodeDepth' is deprecated.
    #> Use 'nodeHeight' instead.
    #> See help("Deprecated")
    #>     N23
    #> 0.77077
    depthTips(g1)
    #> Warning: 'depthTips' is deprecated.
    #> Use 'nodeHeight' instead.
    #> See help("Deprecated")

    #> Warning: 'nodeDepth' is deprecated.
    #> Use 'nodeHeight' instead.
    #> See help("Deprecated")
    #>   fuliginosa       fortis magnirostris  conirostris     scandens   difficilis
    #>      0.88077      0.88077      0.88077      0.88077      0.88077      0.88077
    #>      pallida     parvulus   psittacula       pauper   platyspiza        fusca
    #>      0.88077      0.88077      0.88077      0.88077      0.88077      0.88077
    #> pinaroloxias     olivacea
    #>      0.88077      0.88077

## Trees with data

The `phylo4d` class matches trees with data, or combines them with a data frame to make a `phylo4d` (tree-with-data) object.

Now we’ll take the Geospiza data from `geospiza_raw$data` and merge it with the tree. First, let’s prepare the data:

    g1 <- as(geospiza_raw$tree, "phylo4")
    geodata <- geospiza_raw$data

However, since G. olivacea is included in the tree but not in the data set, we will initially run into some trouble:

    g2 <- phylo4d(g1, geodata)
    #> Error in formatData(phy = x, dt = tip.data, type = "tip", ...): The following nodes are not found in the dataset:  olivacea

To deal with G. olivacea missing from the data, we have a few choices. The easiest is to use to allow to create the new object with a warning (you can also use to proceed without warnings):

    g2 <- phylo4d(g1, geodata, missing.data="warn")
    #> Warning in formatData(phy = x, dt = tip.data, type = "tip", ...): The following nodes are
    #> not found in the dataset: olivacea

Another way to deal with this would be to use `prune()` to drop the offending tip from the tree first:

    g1sub <- prune(g1, "olivacea")
    g1B <- phylo4d(g1sub, geodata)

The difference between the two objects is that the species G. olivacea is still present in the tree but has no data (i.e., `NA`) associated with it. In the other case, G. olivacea is not included in the tree anymore. The approach you choose depends on the goal of your analysis.

You can summarize the new object with the function `summary`. It breaks down the statistics about the traits based on whether it is associated with the tips for the internal nodes: <<geomergesum>>= summary(g2) @

Or use `tdata()` to extract the data (i.e., `tdata(g2)`). By default, `tdata()` will retrieve tip data, but you can also get internal node data only () or — if the tip and node data have the same format — all the data combined ().

If you want to plot the data (e.g. for checking the input), `plot(tdata(g2))` will create the default plot for the data — in this case, since it is a data frame, this will be a `pairs` plot of the data.

## Subsetting

The `subset` command offers a variety of ways of extracting portions of a `phylo4` or `phylo4d` tree, keeping any tip/node data consistent.

tips.include

  give a vector of tips (names or numbers) to retain

tips.exclude

  give a vector of tips (names or numbers) to drop

mrca

  give a vector of node or tip names or numbers; extract the clade containing these taxa

node.subtree

  give a node (name or number); extract the subtree starting from this node

Different ways to extract the fuliginosa-scandens clade:

    subset(g2, tips.include=c("fuliginosa", "fortis", "magnirostris",
      "conirostris", "scandens"))
    subset(g2, node.subtree=21)
    subset(g2, mrca=c("scandens", "fortis"))

One could drop the clade by doing

    subset(g2, tips.exclude=c("fuliginosa", "fortis", "magnirostris",
      "conirostris", "scandens"))
    subset(g2, tips.exclude=names(descendants(g2, MRCA(g2, c("difficilis",
    "fortis")))))

## Tree-walking

`phylobase` provides many functions that allows users to explore relationships between nodes on a tree (tree-walking and tree traversal). Most functions work by specifying the `phylo4` (or `phylo4d`) object as the first argument, the node numbers/labels as the second argument (followed by some additional arguments).

`getNode` allows you to find a node based on its node number or its label. It returns a vector with node numbers as values and labels as names:

    data(geospiza)
    getNode(geospiza, 10)
    #> pauper
    #>     10
    getNode(geospiza, "pauper")
    #> pauper
    #>     10

If no node is specified, they are all returned, and if a node can’t be found it’s returned as a `NA`. It is possible to control what happens when a node can’t be found:

    getNode(geospiza)
    #>   fuliginosa       fortis magnirostris  conirostris     scandens   difficilis
    #>            1            2            3            4            5            6
    #>      pallida     parvulus   psittacula       pauper   Platyspiza        fusca
    #>            7            8            9           10           11           12
    #> Pinaroloxias     olivacea          N15          N16          N17          N18
    #>           13           14           15           16           17           18
    #>          N19          N20          N21          N22          N23          N24
    #>           19           20           21           22           23           24
    #>          N25          N26          N27
    #>           25           26           27
    getNode(geospiza, 10:14)
    #>       pauper   Platyspiza        fusca Pinaroloxias     olivacea
    #>           10           11           12           13           14
    getNode(geospiza, "melanogaster", missing="OK") # no warning
    #> <NA>
    #>   NA
    getNode(geospiza, "melanogaster", missing="warn") # warning!
    #> Warning in getNode(geospiza, "melanogaster", missing = "warn"): Some nodes not found
    #> among all nodes in tree: melanogaster
    #> <NA>
    #>   NA

`children` and `ancestor` give the immediate neighboring nodes:

    children(geospiza, 16)
    #>          N17 Pinaroloxias
    #>           17           13
    ancestor(geospiza, 16)
    #> N15
    #>  15

while `descendants` and `ancestors` can traverse the tree up to the tips or root respectively:

    descendants(geospiza, 16) # by default returns only the tips
    #> Pinaroloxias        fusca   Platyspiza   difficilis     scandens  conirostris
    #>           13           12           11            6            5            4
    #> magnirostris   fuliginosa       fortis      pallida       pauper     parvulus
    #>            3            1            2            7           10            8
    #>   psittacula
    #>            9
    descendants(geospiza, "all") # also include the internal nodes
    #> Warning in getNode(phy, node, missing = "warn"): Some nodes not found among all nodes in
    #> tree: all
    #> named list()
    ancestors(geospiza, 20)
    #> N19 N18 N17 N16 N15
    #>  19  18  17  16  15
    ancestors(geospiza, 20, "ALL") # uppercase ALL includes self
    #> N20 N19 N18 N17 N16 N15
    #>  20  19  18  17  16  15

`siblings` returns the other node(s) associated with the same ancestor:

    siblings(geospiza, 20)
    #> N25
    #>  25
    siblings(geospiza, 20, include.self=TRUE)
    #> N20 N25
    #>  20  25

`MRCA` returns the most common recent ancestor for a set of tips, and shortest path returns the nodes connecting 2 nodes:

    MRCA(geospiza, 1:6)
    #> N20
    #>  20
    shortestPath(geospiza, 4, "pauper")
    #> N19 N20 N21 N22 N25 N26
    #>  19  20  21  22  25  26

## multiPhylo4 classes

`multiPhylo4` classes are not yet implemented but will be coming soon.

## Examples

### Constructing a Brownian motion trait simulator

This section will describe a way of constructing a simulator that generates trait values for extant species (tips) given a tree with branch lengths, assuming a model of Brownian motion.

We can use to coerce the tree into a variance-covariance matrix form, and then use `mvrnorm` from the `MASS` package to generate a set of multivariate normally distributed values for the tips. (A benefit of this approach is that we can very quickly generate a very large number of replicates.) This example illustrates a common feature of working with `phylobase` — combining tools from several different packages to operate on phylogenetic trees with data.

We start with a randomly generated tree using `rcoal()` from `ape` to generate the tree topology and branch lengths:

    set.seed(1001)
    tree <- as(rcoal(12), "phylo4")

Next we generate the phylogenetic variance-covariance matrix (by coercing the tree to a `phylo4vcov` object) and pick a single set of normally distributed traits (using to pick a multivariate normal deviate with a variance-covariance matrix that matches the structure of the tree).

    vmat <- as(tree, "phylo4vcov")
    vmat <- cov2cor(vmat)
    library(MASS)
    trvec <- mvrnorm(1, mu=rep(0, 12), Sigma=vmat)

The last step (easy) is to convert the `phylo4vcov` object back to a `phylo4d` object:

    treed <- phylo4d(tree, tip.data=as.data.frame(trvec))
    plot(treed)

plot of chunk plotvcvphylo

## Definitions/slots

This section details the internal structure of the `phylo4`, `multiphylo4` (coming soon!), `phylo4d`, and `multiphylo4d` (coming soon!) classes. The basic building blocks of these classes are the `phylo4` object and a dataframe. The `phylo4` tree format is largely similar to the one used by `phylo` class in the package `ape`1.

We use “edge” for ancestor-descendant relationships in the phylogeny (sometimes called “branches”) and “edge lengths” for their lengths (“branch lengths”). Most generally, “nodes” are all species in the tree; species with descendants are “internal nodes” (we often refer to these just as “nodes”, meaning clear from context); “tips” are species with no descendants. The “root node” is the node with no ancestor (if one exists).

### phylo4

Like `phylo`, the main components of the `phylo4` class are:

edge

  a 2-column matrix of integers, with \(N\) rows for a rooted tree or \(N-1\) rows for an unrooted tree and column names `ancestor` and `descendant`. Each row contains information on one edge in the tree. See below for further constraints on the edge matrix.

edge.length

  numeric list of edge lengths (length \(N\) (rooted) or \(N-1\) (unrooted) or empty (length 0))

tip.label

  character vector of tip labels (required), with length=# of tips. Tip labels need not be unique, but data-tree matching with non-unique labels will cause an error

node.label

  character vector of node labels, length=# of internal nodes or 0 (if empty). Node labels need not be unique, but data-tree matching with non-unique labels will cause an error

order

  character: “preorder”, “postorder”, or “unknown” (default), describing the order of rows in the edge matrix. , “pruningwise” and “cladewise” are accepted for compatibility with `ape`

The edge matrix must not contain `NA`s, with the exception of the root node, which has an `NA` for `ancestor`. `phylobase` does not enforce an order on the rows of the edge matrix, but it stores information on the current ordering in the slot — current allowable values are “unknown” (the default), “preorder” (equivalent to “cladewise” in `ape`) or “postorder” 2.

The basic criteria for the edge matrix are similar to those of `ape`, as documented it’s tree specification3. This is a modified version of those rules, for a tree with \(n\) tips and \(m\) internal nodes:

- Tips (no descendants) are coded \(1,\ldots, n\), and internal nodes (\(\ge 1\) descendant) are coded \(n + 1, \ldots , n + m\) (\(n + 1\) is the root). Both series are numbered with no gaps.

- The first (ancestor) column has only values \(> n\) (internal nodes): thus, values \(\le n\) (tips) appear only in the second (descendant) column

- all internal nodes (not including the root) must appear in the first (ancestor) column at least once [unlike `ape`, which nominally requires each internal node to have at least two descendants (although it doesn’t absolutely prohibit them and has a function to get rid of them), `phylobase` does allow these “singleton nodes” and has a method `hasSingle` for detecting them]. Singleton nodes can be useful as a way of representing changes along a lineage; they are used this way in the `ouch` package.

- the number of occurrences of a node in the first column is related to the nature of the node: once if it is a singleton, twice if it is dichotomous (i.e., of degree 3 [counting ancestor as well as descendants]), three times if it is trichotomous (degree 4), and so on.

`phylobase` does not technically prohibit reticulations (nodes or tips that appear more than once in the descendant column), but they will probably break most of the methods. Disconnected trees, cycles, and other exotica are not tested for, but will certainly break the methods.

We have defined basic methods for `phylo4`:`show`, `print`, and a variety of accessor functions (see help files). `summary` does not seem to be terribly useful in the context of a “raw” tree, because there is not much to compute.

### phylo4d

The `phylo4d` class extends `phylo4` with data. Tip data, and (internal) node data are stored separately, but can be retrieved together or separately with `tdata(x,"tip")`, `tdata(x,"internal")` or `tdata(x,"all")`. There is no separate slot for edge data, but these can be stored as node data associated with the descendant node.

1. https://emmanuelparadis.github.io/ape_development.html↩︎

2. see https://en.wikipedia.org/wiki/Tree_traversal for more information on orderings. (`ape`’s “pruningwise” is “bottom-up” ordering).↩︎

3. https://emmanuelparadis.github.io/misc/FormatTreeR.pdf↩︎